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Chapter 1.
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[]\OT1/cmr/m/n/10.95 On the fourth \OT1/cmss/m/n/10.95 LiDIA \OT1/cmr/m/n/10.95
 level there are the \OT1/cmr/bx/n/10.95 pa-ram-e-ter-ized classes[] \OT1/cmr/m
/n/10.95 (also called \OT1/cmr/bx/n/10.95 con-tainer classes[]\OT1/cmr/m/n/10.9
5 ).
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Chapter 2.
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\OT1/cmr/m/n/10.95 Add \OT1/cmtt/m/n/10.95 d://LiDIA/include \OT1/cmr/m/n/10.95
 to \OT1/cmtt/m/n/10.95 C[]INCLUDE[]PATH \OT1/cmr/m/n/10.95 and \OT1/cmtt/m/n/1
0.95 CPLUS[]INCLUDE[]PATH \OT1/cmr/m/n/10.95 and add \OT1/cmtt/m/n/10.95 d://Li
DIA/lib/LiDIA/os2/compiler[]name
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Chapter 3.

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[]\OT1/cmtt/m/n/10.95 g++ -O fact.c -I/usr/local/include -L/usr/local/lib/LiDIA
/sparc8-sun-solaris2.5.1/g++
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[]\OT1/cmtt/m/n/10.95 gcc -O2 fact.C -Id:/LiDIA/include -Ld:/LiDIA/lib/LiDIA/os
2/g++ -lLiDIA -lbsd -lstdcpp 
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Chapter 4.

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\OT1/cmr/m/n/10.95 The con-struc-tor \OT1/cmtt/m/n/10.95 bigint(double) \OT1/cm
r/m/n/10.95 was re-placed by the assignment-function \OT1/cmtt/m/n/10.95 void b
igint::assign(double)
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\OT1/cmr/m/n/10.95 us-ing the old lat-tice classes one has to re-place the clas
s names big-int/bigfloat[]lattice[]basis/gensys
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[][]\OT1/cmr/m/n/10.95 The func-tions \OT1/cmtt/m/n/10.95 alg[]number::which[]o
rder()\OT1/cmr/m/n/10.95 , \OT1/cmtt/m/n/10.95 module::which[]order()\OT1/cmr/m
/n/10.95 , and \OT1/cmtt/m/n/10.95 order::which[]field()
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[]\OT1/cmr/m/n/10.95 In the rare cases, where you re-ally need to ob-tain an or
-der or num-ber field, use \OT1/cmtt/m/n/10.95 order(a.which[]base())
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Chapter 5.

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\OT1/cmr/m/n/10.95 and fur-ther-more, the name \OT1/cmtt/m/n/10.95 Lv[]bigint.o
 \OT1/cmr/m/n/10.95 is added to the list \OT1/cmtt/m/n/10.95 CXXOBJ \OT1/cmr/m/
n/10.95 at the end of \OT1/cmtt/m/n/10.95 makefile.inst\OT1/cmr/m/n/10.95 .
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\OT1/cmr/m/n/10.95 When you call \OT1/cmtt/m/n/10.95 make g++ \OT1/cmr/m/n/10.9
5 in that di-rec-tory, the cor-re-spond-ing \OT1/cmtt/m/n/10.95 makefile \OT1/c
mr/m/n/10.95 in-cludes \OT1/cmtt/m/n/10.95 makefile.inst
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[][]\OT1/cmr/m/n/10.95 Edit \OT1/cmtt/m/n/10.95 $(LIDIA[]HOME)/include/LiDIA/ma
th[]vector.h\OT1/cmr/m/n/10.95 ,\OT1/cmtt/m/n/10.95 sort[]vector.h\OT1/cmr/m/n/
10.95 , and \OT1/cmtt/m/n/10.95 file[]vector.h\OT1/cmr/m/n/10.95 :
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Chapter 6.
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\OT1/cmr/m/n/10.95 The mem-ber func-tions \OT1/cmtt/m/n/10.95 scan[]from[]file(
)\OT1/cmr/m/n/10.95 , \OT1/cmtt/m/n/10.95 print[]to[]file()\OT1/cmr/m/n/10.95 ,
 \OT1/cmtt/m/n/10.95 read[]from[]file() \OT1/cmr/m/n/10.95 and \OT1/cmtt/m/n/10
.95 write[]to[]file()
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\OT1/cmr/m/n/10.95 the \OT1/cmtt/m/n/10.95 lidia[]error[]handler \OT1/cmr/m/n/1
0.95 will be in-voked. If the in-verse does not ex-ist and [],
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[]|\OT1/cmr/m/n/10.95 returns a ran-dom \OT1/cmr/bx/n/10.95 big-mod [] \OT1/cmr
/m/n/10.95 with ran-dom man-tissa in the range [].
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[]|\OT1/cmr/m/n/10.95 normalizes the \OT1/cmr/bx/n/10.95 multi[]bigmod [] \OT1/
cmr/m/n/10.95 such that the man-tissa of [] is in the range [],
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\OT1/cmr/m/n/10.95 the \OT1/cmtt/m/n/10.95 lidia[]error[]handler \OT1/cmr/m/n/1
0.95 will be in-voked. If the in-verse does not ex-ist and [],
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[]|\OT1/cmr/m/n/10.95 returns a ran-dom \OT1/cmr/bx/n/10.95 multi[]bigmod [] \O
T1/cmr/m/n/10.95 with ran-dom man-tissa in the range [],
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[]|\OT1/cmr/m/n/10.95 initializes a \OT1/cmr/bx/n/10.95 bigfloat[]int \OT1/cmr/
m/n/10.95 with the re-sult of the float-ing point di-vi-sion of two \OT1/cmr/bx
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[]|[] \OT1/cmr/m/n/10.95 if []. Oth-er-wise the lidia[]error[]handler
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[]|\OT1/cmr/m/n/10.95 returns [] if []. Oth-er-wise the lidia[]error[]handler
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\OT1/cmr/m/n/10.95 ing steps. If [] has not been ini-tial-ized be-fore, this wi
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[]|\OT1/cmr/m/n/10.95 returns the prime with in-dex [] from un-der-ly-ing \OT1/
cmr/bx/n/10.95 crt[]table \OT1/cmr/m/n/10.95 ob-ject. The \OT1/cmtt/m/n/10.95 l
idia[]error[]handler
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[]\OT1/cmr/m/n/10.95 Both val-ues can in-di-vid-u-ally be changed for a vec-tor
 [] by us-ing the func-tions \OT1/cmtt/m/n/10.95 v.set[]capacity()
 []

[117] [118] [119] [120] [121]
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\OT1/cmr/m/n/10.95 A vari-able of type \OT1/cmr/bx/n/10.95 math[]vector[] \OT1/
cmr/m/n/10.95 con-tains the same com-po-nents as \OT1/cmr/bx/n/10.95 base[]vect
or[]
 []

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\OT1/cmr/m/n/10.95 This class pro-vides two stan-dard di-rec-tions \OT1/cmr/bx/
n/10.95 SORT[]VECTOR[]UP \OT1/cmr/m/n/10.95 and \OT1/cmr/bx/n/10.95 SORT[]VECTO
R[]DOWN
 []

[129]
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\OT1/cmr/m/n/10.95 de-fined con-stants SORT[]VECTOR[]UP, SORT[]VECTOR[]UP or SO
RT[]VECTOR[]CMP.
 []


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\OT1/cmr/m/n/10.95 de-fined con-stants SORT[]VECTOR[]UP, SORT[]VECTOR[]DOWN or 
SORT[]VECTOR[]CMP.
 []

[130]
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\OT1/cmr/m/n/10.95 value must be ei-ther of the two con-stants SORT[]VECTOR[]UP
 or SORT[]VECTOR[]DOWN.
 []

[131]
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[]\OT1/cmr/m/n/10.95 An el-e-ment [] can ei-ther be in-serted at a spec-i-fied 
po-si-tion (us-ing the func-tion \OT1/cmtt/m/n/10.95 insert[]at()
 []


Overfull \hbox (28.95631pt too wide) in paragraph at lines 238--238
\OT1/cmr/m/n/10.95 SORT[]VECTOR[]DOWN. If [] dif-fers from these val-ues, the \
OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []

[132]
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\OT1/cmr/m/n/10.95 must be one ei-ther of the two con-stants SORT[]VECTOR[]UP o
r SORT[]VECTOR[]DOWN.
 []


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[]|\OT1/cmr/m/n/10.95 uses the func-tion \OT1/cmtt/m/n/10.95 v.bin[]search() \O
T1/cmr/m/n/10.95 to find [] in [] us-ing the com-pare func-tion \OT1/cmtt/m/n/1
0.95 (*cmp)()\OT1/cmr/m/n/10.95 .
 []

[133]
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[]\OT1/cmr/m/n/10.95 If [] or [] or [] in one of the fol-low-ing con-struc-tors
, the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []

[141]
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[]|\OT1/cmr/m/n/10.95 changes the num-ber of rows of ma-trix [] into []. If [],
 the rows []
 []


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\OT1/cmr/m/n/10.95 with val-ues gen-er-ated by the de-fault con-struc-tor of ty
pe \OT1/cmr/bx/n/10.95 T\OT1/cmr/m/n/10.95 . The \OT1/cmtt/m/n/10.95 lidia[]err
or[]handler
 []

[142]
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[]|\OT1/cmr/m/n/10.95 allocates mem-ory and re-turns a copy of row []. If [] or
 [], the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []


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[]|\OT1/cmr/m/n/10.95 allocates mem-ory and re-turns a copy of row []. If [] or
 [], the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []


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[]|\OT1/cmr/m/n/10.95 copies the val-ues of row [] to \OT1/cmr/bx/n/10.95 base[
]vector []\OT1/cmr/m/n/10.95 . If [] or [] the \OT1/cmtt/m/n/10.95 lidia[]error
[]handler
 []


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[]|\OT1/cmr/m/n/10.95 copies the val-ues of row [] to \OT1/cmr/bx/n/10.95 base[
]vector []\OT1/cmr/m/n/10.95 . If [] or [] the \OT1/cmtt/m/n/10.95 lidia[]error
[]handler
 []


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[]|\OT1/cmr/m/n/10.95 stores [] en-tries of ar-ray [] in row [] of ma-trix [] s
tart-ing at col-umn zero. If []
 []

[143] [144]
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[]|\OT1/cmr/m/n/10.95 stores [] as []. If [] or [] or [] or [], the \OT1/cmtt/m
/n/10.95 lidia[]error[]handler
 []

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[]\OT1/cmr/m/n/10.95 The \OT1/cmr/bx/n/10.95 os-tream \OT1/cmr/m/n/10.95 op-er-
a-tor \OT1/cmtt/m/n/10.95 << \OT1/cmr/m/n/10.95 out-puts the ma-trix in the for
-mat given by the vari-able []
 []

[153]
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\OML/cmm/m/it/10.95 LIDIA \OT1/cmr/m/n/10.95 := \OML/cmm/m/it/10.95 Mat\OT1/cmr
/m/n/10.95 (\OML/cmm/m/it/10.95 Z; \OT1/cmr/m/n/10.95 [[\OML/cmm/m/it/10.95 a[]
;  a[]; [];  a[]\OT1/cmr/m/n/10.95 ]\OML/cmm/m/it/10.95 ;  \OT1/cmr/m/n/10.95 [
\OML/cmm/m/it/10.95 a[]; [];  a[]\OT1/cmr/m/n/10.95 ]\OML/cmm/m/it/10.95 ; []; 
 \OT1/cmr/m/n/10.95 [\OML/cmm/m/it/10.95 a[]; [];  a[]\OT1/cmr/m/n/10.95 ]])
 []

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\OT1/cmr/m/n/10.95 A vari-able of type \OT1/cmr/bx/n/10.95 math[]matrix[] \OT1/
cmr/m/n/10.95 con-tains the same com-po-nents as \OT1/cmr/bx/n/10.95 base[]matr
ix[]\OT1/cmr/m/n/10.95 . 
 []


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[]\OT1/cmr/m/n/10.95 If [] or [] or [] in one of the fol-low-ing con-struc-tors
 the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []

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[]
 []


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[]
 []


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[]
 []


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[]
 []

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\OT1/cmr/m/n/10.95 A vari-able of type \OT1/cmr/bx/n/10.95 big-int[]matrix \OT1
/cmr/m/n/10.95 con-tains the same com-po-nents as a \OT1/cmr/bx/n/10.95 math[]m
atrix[]bigint[]\OT1/cmr/m/n/10.95 . 
 []


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\OT1/cmr/m/n/10.95 prime num-bers. By de-fault, this ta-ble is taken out of the
 file \OT1/cmtt/m/n/10.95 LIDIA[]INSTALL[]DIR/lib/LiDIA/LIDIA[]PRIMES\OT1/cmr/m
/n/10.95 ,
 []


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[]\OT1/cmr/m/n/10.95 If [] or [] or [] in one of the fol-low-ing con-struc-tors
 the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []

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[]|\OT1/cmr/m/n/10.95 sets []. If [] doesn't hold, the \OT1/cmtt/m/n/10.95 lidi
a[]error[]handler
 []

[168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179]
[180]
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[183] [184] [185] [186] [187] [188] [189] [190]
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[]\OT1/cmr/m/n/10.95 For sup-port-ing more in-put and out-put for-mats we sug-g
est to read and write \OT1/cmr/bx/n/10.95 big-int[]matrices
 []

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[][]\OT1/cmr/m/n/10.95 The Fincke-Pohst al-go-rithm for com-put-ing short-est v
ec-tors of a lat-tice []
 []

[193] [194] [195] [196]
Overfull \hbox (40.97163pt too wide) in paragraph at lines 309--313
\OT1/cmr/m/n/10.95 Please note that it is al-lowed to change the pre-ci-sion fo
r \OT1/cmr/bx/n/10.95 bigfloat\OT1/cmr/m/n/10.95 s within \OT1/cmtt/m/n/10.95 v
\OT1/cmr/m/n/10.95 oid (*scal[]bfl)(bigfloat&,
 []

[197] [198] [199]
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\OT1/cmr/m/n/10.95 Please note that it is al-lowed to change the pre-ci-sion fo
r \OT1/cmr/bx/n/10.95 bigfloat\OT1/cmr/m/n/10.95 s within \OT1/cmtt/m/n/10.95 v
\OT1/cmr/m/n/10.95 oid (*scal[]bfl)(bigfloat&,
 []

[200]
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[]|\OT1/cmr/m/n/10.95 these func-tions com-pute the trans-for-ma-tion ma-trix [
] as well as []
 []

[201] [202] [203]
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[]|\OT1/cmr/m/n/10.95 reduces the lat-tice [] by us-ing the al-go-rithm of Benn
e de Weger [[]]. The \OT1/cmtt/m/n/10.95 lidia[]error[]handler
 []

[204]
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[]|\OT1/cmr/m/n/10.95 these func-tions com-pute a []-dimensional re-duced ba-si
s of []
 []

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 []

[205]
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 []\OT1/cmtt/m/n/10.95 void bigfloat_scalar(bigfloat &x, bigfloat *a, bigfloat 
*b, lidia_size_t len)[] 
 []

[206]
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 []    \OT1/cmtt/m/n/10.95 cout << "The lattice was represented by a generating
 system.\n" << endl;[] 
 []


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 []  \OT1/cmtt/m/n/10.95 cout << "Number of reduction steps:\t" << li.lll.reduc
tion_steps << endl;[] 
 []


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 []  \OT1/cmtt/m/n/10.95 cout << "Number of correction steps:\t" << li.lll.corr
ection_steps << endl;[] 
 []

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\OT1/cmr/m/n/10.95 A vari-able of type \OT1/cmr/bx/n/10.95 bigfloat[]lattice \O
T1/cmr/m/n/10.95 co-sists of the same com-po-nents as \OT1/cmr/bx/n/10.95 math[
]matrix[]bigfloat[]\OT1/cmr/m/n/10.95 .
 []

[210] [211] [212] [213]
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\OT1/cmr/m/n/10.95 Please note that it is al-lowed to change the pre-ci-sion fo
r \OT1/cmr/bx/n/10.95 bigfloat\OT1/cmr/m/n/10.95 s within \OT1/cmtt/m/n/10.95 v
\OT1/cmr/m/n/10.95 oid (*scal[]bfl)(bigfloat&,
 []

[214] [215] [216]
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\OT1/cmr/m/n/10.95 Please note that it is al-lowed to change the pre-ci-sion fo
r \OT1/cmr/bx/n/10.95 bigfloat\OT1/cmr/m/n/10.95 s within \OT1/cmtt/m/n/10.95 v
\OT1/cmr/m/n/10.95 oid (*scal[]bfl)(bigfloat&,
 []

[217]
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[]|\OT1/cmr/m/n/10.95 these func-tions com-pute the trans-for-ma-tion ma-trix [
] as well as []
 []

[218] [219] [220] [221] [222] [223]
Overfull \hbox (13.5265pt too wide) in paragraph at lines 625--625
[]|\OT1/cmr/m/n/10.95 these func-tions com-pute a []-dimensional re-duced ba-si
s of []
 []

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Underfull \hbox (badness 10000) in paragraph at lines 634--635

 []


Overfull \hbox (20.4704pt too wide) in paragraph at lines 755--755
 []\OT1/cmtt/m/n/10.95 void bigfloat_scalar(bigfloat &x, bigfloat *a, bigfloat 
*b, lidia_size_t len)[] 
 []

[224]
Overfull \hbox (3.22433pt too wide) in paragraph at lines 755--755
 []    \OT1/cmtt/m/n/10.95 cout << "The lattice was represented by a generating
 system." << endl;[] 
 []

[225]
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 []  \OT1/cmtt/m/n/10.95 cout << "Number of reduction steps:\t" << li.lll.reduc
tion_steps << endl;[] 
 []


Overfull \hbox (20.4704pt too wide) in paragraph at lines 755--755
 []  \OT1/cmtt/m/n/10.95 cout << "Number of correction steps:\t" << li.lll.corr
ection_steps << endl;[] 
 []


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 []\OT1/cmtt/m/n/10.95 (  7.64  -0.15   34.62  26.5  -21.13 )   Reduction param
eter was:     0.99[] 
 []


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 []\OT1/cmtt/m/n/10.95 ( -1.11  -6       6.77    73.79 -0.29  )  Reduction para
meter was:    0.99[] 
 []

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\OT1/cmr/m/n/10.95 A \OT1/cmr/bx/n/10.95 quadratic[]form \OT1/cmr/m/n/10.95 con
-sists of an or-dered triple [] which rep-re-sents the form [].
 []

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 []  \OT1/cmtt/m/n/10.95 cout << "Transforming f with the inverse transformatio
n yields:  " << f ;[] 
 []

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\OT1/cmr/m/n/10.95 ciently ac-cu-rate es-ti-mate from which a value [] can be c
om-puted sat-is-fy-ing []
 []

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\OT1/cmr/m/n/10.95 sen-ta-tion, i.e., an or-dered pair of \OT1/cmr/bx/n/10.95 b
ig-int\OT1/cmr/m/n/10.95 s [] rep-re-sent-ing the []-module [],
 []

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[]| [][] 
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[]|\OT1/cmr/m/n/10.95 sets [] to a re-duced rep-re-sen-ta-tive of the prin-ci-p
al ideal gen-er-ated by [],
 []

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[]|\OT1/cmr/m/n/10.95 returns the value [] cor-re-spond-ing to the rep-re-sen-t
a-tion [],
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\OT1/cmr/m/n/10.95 The ap-pro-pri-ate func-tion \OT1/cmr/bx/n/10.95 power[]imag
 \OT1/cmr/m/n/10.95 of \OT1/cmr/bx/n/10.95 power[]real \OT1/cmr/m/n/10.95 is us
ed, de-pend-ing on whether
 []

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[]| [][] 
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 []  \OT1/cmtt/m/n/10.95 cin >> O;                            // Now the base o
f O is current_base[] 
 []


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 []  \OT1/cmtt/m/n/10.95 O = O.maximize();                    // Now the curren
t_base is the base[] 
 []


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 []      \OT1/cmtt/m/n/10.95 cin >> F;                       // now the base of
 F is the current_base[] 
 []


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 []      \OT1/cmtt/m/n/10.95 // The numbers used in the next iteration will be 
numbers in order(F)!![] 
 []

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[]|[] \OT1/cmr/m/n/10.95 if [] and [] are mem-bers of the same or-der. Oth-er-w
ise the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
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[]|[] \OT1/cmr/m/n/10.95 if [] and [] are mem-bers of the same or-der. Oth-er-w
ise the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
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[]|[] \OT1/cmr/m/n/10.95 if [] and [] are mem-bers of the same or-der. Oth-er-w
ise the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
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\OT1/cmr/m/n/10.95 only suc-cess-ful if \OT1/cmtt/m/n/10.95 a.which[]base() = b
.which[]base()\OT1/cmr/m/n/10.95 , oth-er-wise the \OT1/cmtt/m/n/10.95 lidia[]e
rror[]handler
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[]|[]\OT1/cmr/m/n/10.95 , if [] and if [] and [] are over the same or-der []. O
th-er-wise the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
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[]|[]\OT1/cmr/m/n/10.95 , if [] and if [] and [] are over the same or-der []. O
th-er-wise the \OT1/cmtt/m/n/10.95 lidia[]error[]handler
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[]|[]\OT1/cmr/m/n/10.95 , if [] is an in-vert-ible ideal. Oth-er-wise we set []
 to the mod-ule [].
 []


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[]|\OT1/cmr/m/n/10.95 returns [], if [] is an in-vert-ible ideal. Oth-er-wise w
e re-turn the mod-ule [].
 []


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[]|\OT1/cmr/m/n/10.95 returns [], if [] is an in-vert-ible ideal. Oth-er-wise w
e re-turn the ideal [].
 []

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\OT1/cmr/m/n/10.95 fault the database is read from the file \OT1/cmtt/m/n/10.95
 LIDIA[]INSTALL[]DIR/lib/LiDIA/GF2n.database\OT1/cmr/m/n/10.95 ,
 []

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[]| [][] 
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\OT1/cmr/m/n/10.95 A vari-able of type gf[]p[]element con-sists of a poly-no-mi
al [], which is of type
 []


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[]\OT1/cmtt/m/n/10.95 .degree()[].degree()\OT1/cmr/m/n/10.95 , so that [] can b
e seen as an el-e-ment of
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\OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 polyno
mial[]\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 ,
 and \OT1/cmr/bx/n/10.95 polynomial[]
 []


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[]\OT1/cmr/m/n/10.95 In the fol-low-ing we will de-scribe the ad-di-tional func
-tions of the classes \OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 ,
 []


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\OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 polyno
mial[]\OT1/cmr/m/n/10.95 , and \OT1/cmr/bx/n/10.95 polynomial[]
 []

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[]\OT1/cmr/m/n/10.95 There are au-to-matic up-casts, which con-vert a \OT1/cmr/
bx/n/10.95 polynomial[] \OT1/cmr/m/n/10.95 to a \OT1/cmr/bx/n/10.95 polynomial[
]\OT1/cmr/m/n/10.95 ,
 []


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\OT1/cmr/m/n/10.95 sions from a \OT1/cmr/bx/n/10.95 polynomial[] \OT1/cmr/m/n/1
0.95 to a \OT1/cmr/bx/n/10.95 polynomial[] \OT1/cmr/m/n/10.95 or a \OT1/cmr/bx/
n/10.95 polynomial[]
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[]|\OT1/cmr/m/n/10.95 computes []. Note that this func-tion may also be ap-plie
d to a \OT1/cmr/bx/n/10.95 polynomial[]
 []

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[]\OT1/cmr/m/n/10.95 In the fol-low-ing we will de-scribe the ad-di-tional func
-tions of the class \OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 . 
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\OT1/cmr/m/n/10.95 which the poly-no-mial is de-fined. So, ev-ery el-e-ment of 
the class polynomial[]has
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[][] 
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[] 
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\OT1/cmr/m/n/10.95 sets co-ef-fi-cient of [] to []; if [], all co-ef-fi-cients 
[] of [] with
 []

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\OT1/cmr/m/n/10.95 put vari-ables of type \OT1/cmr/bx/n/10.95 big-int \OT1/cmr/
m/n/10.95 are au-to-mat-i-cally re-duced. In prin-ci-pal, the lidia[]error[]han
dler
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[][] 
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[]\OT1/cmr/m/n/10.95 Assignments to co-ef-fi-cients of poly-no-mi-als via \OT1/
cmtt/m/n/10.95 operator[](lidia[]size[]t) \OT1/cmr/m/n/10.95 (with-out \OT1/cmt
t/m/n/10.95 const\OT1/cmr/m/n/10.95 )
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\OT1/cmr/m/n/10.95 If you need to do a lot of arith-metic mod-ulo a fixed \OT1/
cmr/bx/n/10.95 Fp[]polynomial []\OT1/cmr/m/n/10.95 , build a \OT1/cmr/bx/n/10.9
5 poly[]modulus
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\OT1/cmr/m/n/10.95 If [] is not ini-tial-ized with [] or [], the lidia[]error[]
handler
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[]|\OT1/cmr/m/n/10.95 tries to fac-tor the el-e-ment [] of [] by us-ing \OT1/cm
r/m/it/10.95 TD \OT1/cmr/m/n/10.95 with all primes [] with \OT1/cmr/m/it/10.95 
lower[]bound[]upper[]bound\OT1/cmr/m/n/10.95 .
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[]|\OT1/cmr/m/n/10.95 tries to fac-tor all base el-e-ments of [] with \OT1/cmr/
m/it/10.95 TD \OT1/cmr/m/n/10.95 us-ing all primes [] with \OT1/cmr/m/it/10.95 
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[]|\OT1/cmr/m/n/10.95 tries to fac-tor the num-ber [] with \OT1/cmr/m/it/10.95 
TD \OT1/cmr/m/n/10.95 us-ing all primes [] with \OT1/cmr/m/it/10.95 lower[]boun
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[]|\OT1/cmr/m/n/10.95 tries to fac-tor the num-ber [] with \OT1/cmr/m/it/10.95 
ECM \OT1/cmr/m/n/10.95 us-ing the strat-egy de-scribed in \OT1/cmtt/m/n/10.95 a
.ecm[]comp(i)
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[][]\OT1/cmr/bx/n/10.95 single[]factor[] \OT1/cmr/m/n/10.95 (fac-tor-iza-tion o
f in-te-gers, re-plac-ing \OT1/cmr/bx/n/10.95 ra-tio-nal[]factorization\OT1/cmr
/m/n/10.95 ) 
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\OT1/cmr/m/n/10.95 tors may do a mean-ing-ful com-par-i-sion of the el-e-ments 
rep-re-sented by a \OT1/cmr/bx/n/10.95 sin-gle[]factor[]
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[]|\OT1/cmr/m/n/10.95 returns [], if [] is a prime fac-tor-iza-tion ac-cord-ing
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 []


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[]|\OT1/cmr/m/n/10.95 returns a fac-tor-iza-tion of the el-e-ment of type \OT1/
cmr/bx/n/10.95 T \OT1/cmr/m/n/10.95 rep-re-sented by the \OT1/cmr/bx/n/10.95 si
n-gle[]factor[]
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\OT1/cmr/bx/n/10.95 factorization[]\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 big
-int\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 Fp[]polynomial\OT1/cmr/m/n/10.95 ,
 \OT1/cmr/bx/n/10.95 polynomial[]\OT1/cmr/m/n/10.95 , \OT1/cmr/bx/n/10.95 mod-u
le/ideal 
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\OT1/cmr/m/n/10.95 Including \OT1/cmr/bx/n/10.95 fac-tor-iza-tion.h \OT1/cmr/m/
n/10.95 in an ap-pli-ca-tion al-lows the use of the C++ type \OT1/cmr/bx/n/10.9
5 factorization[]
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[][]\OT1/cmr/m/n/10.95 a unit [], which is au-to-mat-i-cally ex-tracted from al
l bases (see func-tion \OT1/cmtt/m/n/10.95 extract[]unit()
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[]|\OT1/cmr/m/n/10.95 sorts the fac-tor-iza-tion [] and col-lects equal bases, 
such that [],
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[]|\OT1/cmr/m/n/10.95 refines the fac-tor-iza-tion [] such that the bases of []
 are pair-wise co-prime, i.e. []
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[]|\OT1/cmr/m/n/10.95 returns [], if [] is a prime fac-tor-iza-tion ac-cord-ing
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\OT1/cmtt/m/n/10.95 polynomial[]& 
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[]|\OT1/cmr/m/n/10.95 returns the com-plete fac-tor-iza-tion of [] us-ing a DDF
 ac-cord-ing to Can-tor/Zassenhaus,
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\OT1/cmtt/m/n/10.95 polynomial[]& 
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\OT1/cmr/m/n/10.95 able, [], as it is nec-es-sary if the mem-ber func-tion \OT1
/cmtt/m/n/10.95 a.set[]coeff(T & x ,lidia[]size[]t)
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\OT1/cmr/m/n/10.95 turns a pointer to the al-lo-cated mem-ory. The mem-ory is s
et to zero. For \OT1/cmtt/m/n/10.95 allocate(NMEMB,
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[]|\OT1/cmr/m/n/10.95 allocates [] bytes and re-turns a pointer to the al-lo-ca
ted mem-ory. \OT1/cmtt/m/n/10.95 allocate[]atomic(SIZE)
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\OT1/cmr/m/n/10.95 In the fol-low-ing let \OT1/cmtt/m/n/10.95 xxx \OT1/cmr/m/n/
10.95 stand for \OT1/cmtt/m/n/10.95 lidia[]warning, lidia[]error, lidia[]memory
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[]\OT1/cmr/m/n/10 If you ob-tain \OT1/cmss/m/n/10 LiDIA \OT1/cmr/m/n/10 please 
send us a short no-tice to that ef-fect, e.g., an e-mail mes-sage to \OT1/cmtt/
m/n/10 lidia@cs.uni-sb.de
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[][]\OT1/cmr/m/n/10.95 S.B. Lipp-man: \OT1/cmr/m/it/10.95 C++ Primer\OT1/cmr/m/
n/10.95 . Addison-Wesley Pub-lish-ing Com-pany, 1989,
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[]\OT1/cmr/m/n/10 polynomial over big-int, bi-gra-tional, bigfloat, big-
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